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Parallel-Beam Interferometry With Incoherent Light

It should be possible to achieve resolution beyond the
diffraction limit.

NASA's Jet Propulsion Laboratory, Pasadena, California

A technique of parallel-beam interferometry
with spatially incoherent light has been proposed to solve two problems that
arise in conjunction with using interferometry to measure the shape of a surface.
The first problem is how to obtain spatial resolution in excess of the diffraction
limit; the second problem is how to measure the variation in the shape of an
object with temperature.

Figure 1 illustrates the principle of operation. Spatially
incoherent light (e.g., light from an incandescent lamp) would be collimated,
then made to pass through beam-splitting-and-combining optics that would split
the light into two parallel beams aimed toward the object of interest. These
optics would be adjustable to a change the distance between the two beams. The
light reflected by the object would pass back through the beam-splitting-and-combining
optics which combine the two beams back into a single beam, then through imaging
optics into a camera. Objective optics may or may not be used, as explained
below.

The technique can be characterized as one that utilizes speckle
interferometry with a variable speckle. The splitting of the source incoherent
beam into two parallel beams introduces a delta-function spatial coherence that
gives rise to a speckle interference in the camera. The speckle pattern is measured
as the distance between the two beams is changed. The change in distance changes
the location of the delta function in the spatial coherence, and a spatial autocorrelation
function is measured. The surface of the object of interest can be determined
accurately from the autocorrelation function. Under ideal conditions, resolution
beyond the diffraction limit can be achieved.

The solution to the second problem would have to involve utilization
of the speckle interferometry in a way that would make it unnecessary to scan
the beams. One such way would be to form more than one interference pattern
by use of more than two beams, in a generalization of the basic concept that
involves several two-beam interferometers working together.

Figure 2 presents an example of a parallel-beam interferometer
according to the proposal. A collimated beam of light would pass through an
assembly of beam splitters and prisms. The first beam splitter together with
the second beam splitter would cause both beams to traverse the same path (and
thus the same path length) in opposite directions; this would ensure that white-light
fringes would be imaged on the camera. The objective optics may or may not be
used, depending on the required numerical aperture, which, in turn, would determine
the diffraction-limited imaging resolution. The two beam splitters and the right-angle
prism would be moved together to change the distance between the two beams without
changing the difference between their optical-path lengths.

In addition to resolution beyond the diffraction
limit, the
proposed technique would afford several other advantages over prior interferometric
imaging techniques:

1. The distance to the object could be set arbitrarily.

2. The alignment of the object with the interferometer would
be simplified.

3. Because the two beams would be of the same magnitude, regardless
of the reflectivity of the object, the visibility of the fringes would be relatively
high.

4. Because the two beams would travel along nearly the same
path, effects of variations in the index of refraction of air would be relatively
small. Only high-frequency index variations like those associated with turbulence
would be problematic.

5. Imaging could be done with very small numerical apertures,
so that it would be possible to use working distance longer and optics smaller
than those customarily used.

Figure 1. In Parallel-Beam Interferometry, an object would be illuminated
with two closely spaced, parallel beams generated by splitting a single input
beam. The distance between the parallel beams would be adjustable in any direction
in the plane perpendicular to the axis of propagation.

Figure 2. This Optical Layout is one of several candidate
layouts for a practical parallel-beam interferometer. The two nonpolarizing
beam splitters and the prism would be moved in coordination to adjust the distance
between the parallel beams.

This work was done by Roman C. Gutierrez
of Caltech for NASA's Jet Propulsion Laboratory. For further information,
access the Technical Support Package (TSP) free on-line at www.nasatech.com
under the Physical Sciences category.

In accordance with Public Law 96-517, the contractor has
elected
to retain title to this invention. Inquiries concerning rights for its commercial
use should be addressed to

Technology Reporting Office

JPL

Mail Stop 122-116

4800 Oak Grove Drive

Pasadena, CA 91109

(818) 354-2240

Refer to NPO-20687, volume and number of this NASA Tech
Briefs issue, and the page number.